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Riemann-Hurwitz formula
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For a degree-
d
holomorphic map,
2
g
X
−
2
=
d
(
2
g
Y
−
2
)
+
∑
(
e
p
−
1
)
.
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Compactification of y squared equals x to the eighth minus one
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Product surface without low-genus curves
Ramification divisor